Multi-bit encoding of radio frequency (RF) signals is known in the art. Such encoding is possible by dividing the parameters (e.g., phase and/or amplitude) of the radio signal into a constellation of discrete values with each discrete value (symbol) representative of a particular bit sequence. Examples of such systems include quadrature phase shift keying (QPSK) modulation, or quadrature amplitude modulation (QAM).
Under QPSK, successive two-bit sequences may be communicated to a receiver based upon the phase of the transmitted symbol (e.g., a symbol with a phase in the first quadrant is representative of the bit sequence 00, a symbol with a phase in the second quadrant is representative of the bit sequence 10, etc.). FIG. 1 shows a QPSK constellation diagram.
Because the RF transmission medium is noisy, bit errors are likely to occur in the receiver. Encoding (sometimes referred to as channel encoding) is a well known method for reducing the probability of bit errors in the receiver. Convolutional encoding is a well known and effective encoding method. Convolutional encoding, a type of forward error correction coding, is also typically used with QPSK as a method of enhancing the recoverability of the data which was encoded. Decoding of a convolutionally encoded signal is often accomplished using a maximum likelihood decoder. Maximum likelihood decoding, in such a case, can be efficiently accomplished using the Viterbi algorithm (see Error Correction Coding for Digital Communications, by George C. Clark and J. Bibb Cain, Plenum Press).
Maximum likelihood decoding improves the accuracy of the decoded data by comparing a sequence of received symbols with each sequence of a known constellation of symbols that may have been transmitted. Each of the possible transmitted sequences is generally known as a codeword. The possible codewords are defined by the encoding method The comparison process selects the codeword closest to the received signal sequence (i.e., the codeword with the smallest total Euclidean distance separating the received symbol sequence and the codeword). Choosing the codeword such that the total Euclidean distance to the received symbol sequence is minimized corresponds to maximizing the cumulative likelihood or log-likelihood metric.
If all input message sequences are equally likely, a decoder that achieves the minimum probability of error is one that compares the conditional probabilities, also called the likelihood functions, P(Z.vertline.U.sup.(m)), where Z is the received sequence and U.sup.(m) is one of the possible transmitted sequences, and chooses the sequence with the maximum cumulative log-likelihood metric. The decoder chooses U.sup.(m ) if P(Z.vertline.U.sup.(m ) =max P(Z.vertline.U.sup.(m)) for all U.sup.(m).
For each symbol within the symbol constellation, a metric is calculated by comparing the received symbol with this constellation symbol. This process is repeated for each symbol within the symbol constellation to form a metric set for each received symbol. For each codeword, a metric sequence is then identified through the metric sets. Within each metric sequence, the metric selected from each metric set is the metric associated with each symbol of the codeword. The metrics of each metric sequence are summed and the metric sequence with the largest sum is selected as the most likely. The codeword associated with the selected metric sequence is output the most likely codeword.
The above describes maximum likelihood decoding in its most general sense. In practical applications, maximum likelihood decoders have been designed for a zero-mean Gaussian channel. The effectiveness of such decoding is dependent upon a channel where the noise component of a received signal is a zero-mean Gaussian random variable. To ensure that the noise component is a zero-mean Gaussian random variable, the prior art has taught that a linear receiver must be used, since a linearly processed Gaussian random variable remains a Gaussian random variable. However, in a linear receiver, amplitude variations caused by fading or other short-term atmospheric perturbations must be controlled through the use of automatic gain control (AGC) circuitry in order to keep the received signal within the linear operating range of the receiver. Because of the difficulty and expense of constructing and maintaining linear receivers with AGC circuits, a need exists for a method of maximum likelihood decoding that works with a non-linear receiver (e.g., an amplitude limited, also known as a hard-limiting, receiver).